Question

The pH of the monoacidic base is 12.6990. The molarity of the base is?
(A) 0.02 moles/litre
(B) 0.05 moles/litre
(C) 0.5 moles/litre
(D) 0.2 moles/litre

Answer 1

Hint: The concentration of $O{{H}^{-}}$ ions play a huge role in finding the molarity of bases. The dissociation constant gives us the ratio of products and reactants at equilibrium. Molarity is defined as moles/L of a solution. Bases dissociate to give $O{{H}^{-}}$ ions. Also, pH gives us the information of ${{H}^{+}}$ ions only but we can find the concentration of $O{{H}^{-}}$ ions also.

Complete step by step solution:
-Weak electrolytes cannot dissociate completely into their respective ions. So their ionization is less than 100%. Weak acids, weak bases and sparingly soluble salts come under this category.
Eg.-1. Weak acids like formic acid, acetic acid, hydrogen sulfide are weak electrolytes.
2.Weak bases like ammonia, pyridine and other nitrogen ring bases are weak electrolytes.
3.Salts like AgCl and $BaS{{O}_{4}}$ are weak electrolytes.
-The reaction is feasible only when strong acids and strong bases react to give weak conjugate acids/bases. So, equilibrium of the reaction proceeds in that direction only where strong electrolytes are converted to weak electrolytes. This is why dissociation constant is calculated.
-Acidic strength is the tendency to give ${{H}^{+}}$ ions and basic strength is the tendency to give $O{{H}^{-}}$ ions. This is where pH scale comes into picture. It is defined as the negative logarithm of concentration of ${{H}^{+}}$ions.
$pH=-\log \left[ {{H}^{+}} \right]\text{ or pH= -log}\left[ {{H}_{3}}{{O}^{+}} \right]$
Dissociation constant for a base is given as
$\begin{align}
& {{A}^{-}}+{{H}_{2}}O\rightleftharpoons HA+O{{H}^{-}} \\
& \text{where }{{\text{K}}_{b}}=\dfrac{\left[ HA \right]\left[ O{{H}^{-}} \right]}{\left[ {{A}^{-}} \right]} \\
\end{align}$
-For a given acid or base, pH+pOH=14 and is denoted as $p{{K}_{w}}$ and is called self-ionization constant of water. Also, there is no physical dimension of the dissociation constant although it may appear to have the unit of concentration.
-In the question, we have been given pH of monoacidic base = 12.6990. Now from the relation pH+pOH=14, we can find pOH.
pOH=14-12.6990=1.3310.
Also, from the definition of pOH, we know
pOH= -log$\left[ O{{H}^{-}} \right]$
So, $\left[ O{{H}^{-}} \right]$= 0.05M which is the molarity of the base.

Therefore the correct option is B.

Note: The degree of dissociation of an electrolyte is the fraction of one mole of electrolyte which has dissociated under the given set of conditions. It depends on the nature of the electrolyte, nature of solvent, dilution, pressure and temperature. It is denoted as $\alpha $.